NeurIPS 2025 Papers

360-degree monocular depth estimation plays a crucial role in scene understanding owing to its 180-degree by 360-degree field-of-view (FoV). To mitigate the distortions brought by equirectangular projection, existing methods typically divide 360-degree images into distortion-less perspective patches. However, since these patches are processed independently, depth inconsistencies are often introduced due to scale drift among patches. Recently, video depth estimation (VDE) models have leveraged temporal consistency for stable depth predictions across frames. Inspired by this, we propose to represent a 360-degree image as a sequence of perspective frames, mimicking the viewpoint adjustments users make when exploring a 360-degree scenario in virtual reality. Thus, the spatial consistency among perspective depth patches can be enhanced by exploiting the temporal consistency inherent in VDE models. To this end, we introduce a training-free pipeline for 360-degree monocular depth estimation, called ST²360D. Specifically, ST²360D transforms a 360-degree image into perspective video frames, predicts video depth maps using VDE models, and seamlessly merges these predictions into a complete 360-degree depth map. To generate sequenced perspective frames that align with VDE models, we propose two tailored strategies. First, a spherical-uniform sampling (SUS) strategy is proposed to facilitate uniform sampling of perspective views across the sphere, avoiding oversampling in polar regions typically with limited structural details. Second, a latitude-guided scanning (LGS) strategy is introduced to organize the frames into a coherent sequence, starting from the equator, prioritizing low-latitude slices, and progressively moving toward higher latitudes. Extensive experiments demonstrate that ST²360D achieves strong zero-shot capability on several datasets, supporting resolutions up to 4K.

We consider the empirical distribution of the embeddings of a $k$-layer polynomial GNN on a semi-supervised node classification task and prove a central limit theorem for them. Assuming a community based model for the underlying graph, with growing average degree $\nu_n\to\infty$, we show that the empirical distribution of the centered features, when scaled by $\nu_{n}^{k-1/2}$ converge in 1-Wasserstein distance to a centered stable mixture of multivariate normal distributions. In addition, the joint empirical distribution of uncentered features and labels when normalized by $\nu_n^k$ approach that of mixture of multivariate normal distributions, with stable means and covariance matrices vanishing as $\nu_n^{-1}$. We explicitly identify the asymptotic means and covariances, showing that the mixture collapses towards a 1-D version as $k$ is increased. Our results provides a precise and nuanced lens on how oversmoothing presents itself in the large graph limit, in the sparse regime. In particular, we show that training with cross-entropy on these embeddings is asymptotically equivalent to training on these nearly collapsed Gaussian mixtures.

In pattern classification, efficient uncertainty reasoning plays a critical role, particularly in real-time applications involving noisy data, ambiguous class boundaries, or overlapping categories. Leveraging the advanced computational power of quantum computing, an Adaptive Quantum Circuit for Dempster’s Rule of Combination (AQC-DRC) is proposed to address efficient classification under uncertain environments. The AQC-DRC is developed within the framework of quantum evidence theory (QET) and facilitates decision-making based on quantum basic probability and plausibility levels, which is a generalized Bayesian inference method. The AQC-DRC provides a deterministic computation of DRC, ensuring that quantum fusion outcomes in uncertain pattern classification are exactly aligned with those of the classical method, while simultaneously achieving exponential reductions in the computational complexity of evidence combination and significantly improving fusion efficiency. It is founded that the quantum basic probability amplitude function in QET, as a generalized quantum probability amplitude, can be naturally utilized to express the quantum amplitude encoding. In addition, the quantum basic probability in QET, as a generalized quantum probability, naturally forms a quantum basic probability distribution and can be used to represent quantum measurement outcomes for quantum basic probability level decision-making. Furthermore, the quantum plausibility function in QET also can be naturally used to express the quantum measurement outcomes for quantum plausibility level decision-making. These findings enrich the physical understanding of quantum amplitude encoding and quantum measurement outcomes, offering broad application prospects for representing and processing uncertain knowledge in pattern classification.

Recent work has formalized the reward hypothesis through the lens of expected utility theory, by interpreting reward as utility. Hausner's foundational work showed that dropping the continuity axiom leads to a generalization of expected utility theory where utilities are lexicographically ordered vectors of arbitrary dimension. In this paper, we extend this result by identifying a simple and practical condition under which preferences in a Markov Decision Process (MDP) cannot be represented by scalar rewards, necessitating a 2-dimensional reward function. We provide a full characterization of such reward functions, as well as the general d-dimensional case under a memorylessness assumption on preferences. Furthermore, we show that optimal policies in this setting retain many desirable properties of their scalar-reward counterparts, while in the Constrained MDP (CMDP) setting — another common multiobjective setting — they do not.

Central banks around the world play a crucial role in maintaining economic stability. Deciphering policy implications in their communications is essential, especially as misinterpretations can disproportionately impact vulnerable populations. To address this, we introduce the World Central Banks (WCB) dataset, the most comprehensive monetary policy corpus to date, comprising over 380k sentences from 25 central banks across diverse geographic regions, spanning 28 years of historical data. After uniformly sampling 1k sentences per bank (25k total) across all available years, we annotate and review each sentence using dual annotators, disagreement resolutions, and secondary expert reviews. We define three tasks: Stance Detection, Temporal Classification, and Uncertainty Estimation, with each sentence annotated for all three. We benchmark seven Pretrained Language Models (PLMs) and nine Large Language Models (LLMs) (Zero-Shot, Few-Shot, and with annotation guide) on these tasks, running 15,075 benchmarking experiments. We find that a model trained on aggregated data across banks significantly surpasses a model trained on an individual bank's data, confirming the principle *"the whole is greater than the sum of its parts."* Additionally, rigorous human evaluations, error analyses, and predictive tasks validate our framework's economic utility. Our artifacts are accessible through the HuggingFace and GitHub under the CC-BY-NC-SA 4.0 license.

The constant $\large \pi$ has fascinated scholars throughout the centuries, inspiring numerous formulas for its evaluation, such as infinite sums and continued fractions. Despite their individual significance, many of the underlying connections among formulas remain unknown, missing unifying theories that could unveil deeper understanding. The absence of a unifying theory reflects a broader challenge across math and science: knowledge is typically accumulated through isolated discoveries, while deeper connections often remain hidden. In this work, we present an automated framework for the unification of mathematical formulas. Our system combines large language models (LLMs) for systematic formula harvesting, an LLM-code feedback loop for validation, and a novel symbolic algorithm for clustering and eventual unification. We demonstrate this methodology on the hallmark case of $\large \pi$, an ideal testing ground for symbolic unification. Applying this approach to 455,050 arXiv papers, we validate 385 distinct formulas for $\large \pi$ and prove relations between 360 (94\%) of them, of which 166 (43\%) can be derived from a single mathematical object—linking canonical formulas by Euler, Gauss, Brouncker, and newer ones from algorithmic discoveries by the Ramanujan Machine. Our method generalizes to other constants, including $e$, $\zeta(3)$, and Catalan’s constant, demonstrating the potential of AI-assisted mathematics to uncover hidden structures and unify knowledge across domains.

A variety of recent methods guide large language model outputs via the inference-time addition of *steering vectors* to residual-stream or attention-head representations. In contrast, we propose to inject steering vectors directly into the query and value representation spaces within attention heads. We provide evidence that a greater portion of these spaces exhibit high linear discriminability of concepts --a key property motivating the use of steering vectors-- than attention head outputs. We analytically characterize the effect of our method, which we term *DISentangled COmmunication (DISCO) Steering*, on attention head outputs. Our analysis reveals that DISCO disentangles a strong but underutilized baseline, steering attention head inputs, which implicitly modifies queries and values in a rigid manner. In contrast, DISCO's direct modulation of these components enables more granular control. We find that DISCO achieves superior performance over a number of steering vector baselines across multiple datasets on LLaMA 3.1 8B and Gemma 2 9B, with steering efficacy scoring up to $19.1$% higher than the runner-up. Our results support the conclusion that the query and value spaces are powerful building blocks for steering vector methods. Our code is publicly available at https://github.com/MaxTorop/DISCO.

Prohibited item detection based on X-ray images is one of the most effective security inspection methods. However, the foreground-background feature coupling caused by the overlapping phenomenon specific to X-ray images makes general detectors designed for natural images perform poorly. To address this issue, we propose a Category Semantic Prior Contrastive Learning (CSPCL) mechanism, which aligns the class prototypes perceived by the classifier with the content queries to correct and supplement the missing semantic information responsible for classification, thereby enhancing the model sensitivity to foreground features. To achieve this alignment, we design a specific contrastive loss, CSP loss, which comprises the Intra-Class Truncated Attraction (ITA) loss and the Inter-Class Adaptive Repulsion (IAR) loss, and outperforms classic contrastive losses. Specifically, the ITA loss leverages class prototypes to attract intra-class content queries and preserves essential intra-class diversity via a gradient truncation function. The IAR loss employs class prototypes to adaptively repel inter-class content queries, with the repulsion strength scaled by prototype-prototype similarity, thereby improving inter-class discriminability, especially among similar categories. CSPCL is general and can be easily integrated into Deformable DETR-based models. Extensive experiments on the PIXray, OPIXray, PIDray, and CLCXray datasets demonstrate that CSPCL significantly enhances the performance of various state-of-the-art models without increasing inference complexity. The code is publicly available at https://github.com/Limingyuan001/CSPCL.

The Schrödinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting (IMF) have been proposed—alongside practical approximations like Diffusion Schrödinger Bridge and its Matching (DSBM) variant. While previous work have established asymptotic convergence guarantees for IMF, a quantitative, non-asymptotic understanding remains unknown. In this paper, we provide the first non-asymptotic exponential convergence guarantees for IMF under mild structural assumptions on the reference measure and marginal distributions, assuming a sufficiently large time horizon. Our results encompass two key regimes: one where the marginals are log-concave, and another where they are weakly log-concave. The analysis relies on new contraction results for the Markovian projection operator and paves the way to theoretical guarantees for DSBM.

Large Language Model (LLM) inference is typically memory-intensive, especially when processing large batch sizes and long sequences, due to the large size of key-value (KV) cache. Vector Quantization (VQ) is recently adopted to alleviate this issue, but we find that the existing approach is susceptible to distribution shift due to its reliance on calibration datasets. To address this limitation, we introduce $\textbf{NSNQuant}$, a calibration-free Vector Quantization (VQ) technique designed for low-bit compression of the KV cache. By applying a three-step transformation—$\textbf{1)}$ a token-wise normalization ($\textbf{N}$ormalize), $\textbf{2)}$ a channel-wise centering ($\textbf{S}$hift), and $\textbf{3)}$ a second token-wise normalization ($\textbf{N}$ormalize)—with Hadamard transform, NSNQuant effectively aligns the token distribution with the standard normal distribution. This alignment enables robust, calibration-free vector quantization using a single reusable codebook. Extensive experiments show that NSNQuant consistently outperforms prior methods in both 1-bit and 2-bit settings, offering strong generalization and up to 3$\times$ throughput gains over full-precision baselines.

Computationally resolving turbulence remains a central challenge in fluid dynamics due to its multi-scale interactions. Fully resolving large-scale turbulence through direct numerical simulation (DNS) is computationally prohibitive, motivating data-driven machine learning alternatives. In this work, we propose EddyFormer, a Transformer-based spectral-element (SEM) architecture for large-scale turbulence simulation that combines the accuracy of spectral methods with the scalability of the attention mechanism. We introduce an SEM tokenization that decomposes the flow into grid-scale and subgrid-scale components, enabling capture of both local and global features. We create a new three-dimensional isotropic turbulence dataset and train EddyFormer to achieves DNS-level accuracy at 256^3 resolution, providing a 30x speedup over DNS. When applied to unseen domains up to 4x larger than in training, EddyFormer preserves accuracy on physics-invariant metrics-energy spectra, correlation functions, and structure functions-showing domain generalization. On The Well benchmark suite of diverse turbulent flows, EddyFormer resolves cases where prior ML models fail to converge, accurately reproducing complex dynamics across a wide range of physical conditions.

Proper initialization is critical for Recurrent Neural Networks (RNNs), particularly in long-range reasoning tasks, where repeated application of the same weight matrix can cause vanishing or exploding signals. A common baseline for linear recurrences is Glorot initialization, designed to ensure stable signal propagation---but derived under the infinite-width, fixed-length regime—an unrealistic setting for RNNs processing long sequences. In this work, we show that Glorot initialization is in fact unstable: small positive deviations in the spectral radius are amplified through time and cause the hidden state to explode. Our theoretical analysis demonstrates that sequences of length $t = O(\sqrt{n})$, where $n$ is the hidden width, are sufficient to induce instability. To address this, we propose a simple, dimension-aware rescaling of Glorot that shifts the spectral radius slightly below one, preventing rapid signal explosion or decay. These results suggest that standard initialization schemes may break down in the long-sequence regime, motivating a separate line of theory for stable recurrent initialization.

Reward models are central to aligning LLMs with human preferences, but they are costly to train, requiring large-scale human-labeled preference data and powerful pretrained LLM backbones. Meanwhile, the increasing availability of high-quality synthetic instruction-following datasets raises the question: can simpler, reference-based metrics serve as viable alternatives to reward models during RL-based alignment? In this paper, we show first that BLEU, a basic string-matching metric, surprisingly matches strong reward models in agreement with human preferences on general instruction-following datasets. Based on this insight, we develop BLEUBERI, a method that first identifies challenging instructions and then applies Group Relative Policy Optimization (GRPO) using BLEU directly as the reward function. We demonstrate that BLEUBERI-trained models are competitive with models trained via reward model-guided RL across four challenging instruction-following benchmarks and three different base language models. A human evaluation further supports that the quality of BLEUBERI model outputs is on par with those from reward model-aligned models. Moreover, BLEUBERI models generate outputs that are more factually grounded than competing methods. Overall, we show that given access to high-quality reference outputs (easily obtained via existing instruction-following datasets or synthetic data generation), string matching-based metrics are cheap yet effective proxies for reward models during alignment. We release our code and data at https://github.com/lilakk/BLEUBERI.

Algorithm configuration, which involves selecting algorithm parameters based on sampled problem instances, is a crucial step in applying modern algorithms such as SAT solvers. Although prior work has attempted to understand the theoretical foundations of algorithm configuration, we still lack a comprehensive understanding of why practical algorithm configurators exhibit strong generalization performances in real-world scenarios. In this paper, through the lens of machine learning theory, we provide an algorithm-dependent generalization bound for the widely used model-based algorithm configurators under mild assumptions. Our approach is based on the algorithmic stability framework for generalization bounds. To the best of our knowledge, this is the first generalization bound that applies to a model closely approximating practical model-based algorithm configurators.

Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gröbner and Border bases are fundamental but suffer from high computational costs, which have motivated recent Deep Learning approaches to improve efficiency, albeit at the expense of output correctness. In this work, we introduce the Oracle Border Basis Algorithm, the first Deep Learning approach that accelerates Border basis computation while maintaining output guarantees. To this end, we design and train a Transformer-based oracle that identifies and eliminates computationally expensive reduction steps, which we find to dominate the algorithm's runtime. By selectively invoking this oracle during critical phases of computation, we achieve substantial speedup factors of up to 3.5x compared to the base algorithm, without compromising the correctness of results. To generate the training data, we develop a sampling method and provide the first sampling theorem for border bases. We construct a tokenization and embedding scheme tailored to monomial-centered algebraic computations, resulting in a compact and expressive input representation, which reduces the number of tokens to encode an $n$-variate polynomial by a factor of $O(n)$. Our learning approach is data efficient, stable, and a practical enhancement to traditional computer algebra algorithms and symbolic computation.

Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic statistical guarantees beyond convergence remain limited. In this paper, we present two generalized Gaussian approximation results for local SGD and explore their implications. First, we prove a Berry-Esseen theorem for the final local SGD iterates, enabling valid multiplier bootstrap procedures. Second, motivated by robustness considerations, we introduce two distinct time-uniform Gaussian approximations for the entire trajectory of local SGD. The time-uniform approximations support Gaussian bootstrap-based tests for detecting adversarial attacks. Extensive simulations are provided to support our theoretical results.

Recent research has increasingly focused on reconciling the reasoning capabilities of System 2 with the efficiency of System 1. While existing training-based and prompt-based approaches face significant challenges in terms of efficiency and stability, model merging emerges as a promising strategy to integrate the diverse capabilities of different Large Language Models (LLMs) into a unified model. However, conventional model merging methods often assume uniform importance across layers, overlooking the functional heterogeneity inherent in neural components. To address this limitation, we propose \textbf{A}ctivation-Guided \textbf{C}onsensus \textbf{M}erging (\textbf{ACM}), a plug-and-play merging framework that determines layer-specific merging coefficients based on mutual information between activations of pre-trained and fine-tuned models. ACM effectively preserves task-specific capabilities without requiring gradient computations or additional training. Extensive experiments on Long-to-Short (L2S) and general merging tasks demonstrate that ACM consistently outperforms all baseline methods. For instance, in the case of Qwen-7B models, TIES-Merging equipped with ACM achieves a \textbf{55.3\%} reduction in response length while simultaneously improving reasoning accuracy by \textbf{1.3} points. We submit the code with the paper for reproducibility, and it will be publicly available.

Scenario-based testing is essential for validating the performance of autonomous driving (AD) systems. However, such testing is limited by the scarcity of long-tailed, safety-critical scenarios in existing datasets collected in the real world. To tackle the data issue, we propose the Adv-BMT framework, which augments real-world scenarios with diverse and realistic adversarial interactions. The core component of Adv-BMT is a bidirectional motion transformer (BMT) model to perform inverse traffic motion predictions, which takes the last frame of the scenario as input and reconstruct the traffic in the inverse of chronological order, till the initial time step. The Adv-BMT framework is a two-stage pipeline: it first conducts adversarial initializations and then inverse motion predictions. Different from previous work, we do not need any collision data for pretraining and are still able to generate realistic and diverse collision interactions. Our experimental results validate the quality of generated collision scenarios by Adv-BMT: training in our augmented dataset would reduce episode collision rates by 20\% compared to previous work. The code will be made available.

Existing frameworks for evaluating long-context language models (LCLM) can be broadly categorized into real-world applications (e.g, document summarization) and synthetic tasks (e.g, needle-in-a-haystack). Despite their utility, both approaches are accompanied by certain intrinsic limitations. Real-world tasks often involve complexity that makes interpretation challenging and suffer from data contamination, whereas synthetic tasks frequently lack meaningful coherence between the target information ("needle") and its surrounding context ("haystack"), undermining their validity as proxies for realistic applications. In response to these challenges, we posit that an ideal long-context evaluation framework should be characterized by three essential features: 1) seamless context: coherent contextual integration between target information and its surrounding context; 2) controllable setting: an extensible task setup that enables controlled studies—for example, incorporating additional required abilities such as numerical reasoning; and 3) sound evaluation: avoiding LLM-as-Judge and conduct exact-match to ensure deterministic and reproducible evaluation results. This study introduces $\textbf{LongBioBench}$, a benchmark that utilizes artificially generated biographies as a controlled environment for assessing LCLMs across dimensions of $\textit{understanding}$, $\textit{reasoning}$, and $\textit{trustworthiness}$. Our experimental evaluation, which includes $\textbf{18}$ LCLMs in total, demonstrates that most models still exhibit deficiencies in semantic understanding and elementary reasoning over retrieved results and are less trustworthy as context length increases. Our further analysis indicates some design choices employed by existing synthetic benchmarks, such as contextual non-coherence, numerical needles, and the absence of distractors, rendering them vulnerable to test the model's long-context capabilities. Moreover, we also reveal that long-context continual pretraining primarily adjusts RoPE embedding to accommodate extended context lengths, which in turn yields only marginal improvements in the model’s true capabilities. To sum up, compared to previous synthetic benchmarks, LongBioBench achieves a better trade-off between mirroring authentic language tasks and maintaining controllability, and is highly interpretable and configurable.